Here's a summary of what the waves look like for the three cases on the previous page, the falcon slower than, equal to, and faster than the wave. (If you'd like to see these animated by other sites using various Web techniques, try Animated GIFs (may take a few seconds to load, but works with most any Browser), movie animation (requires an AVI player, which you probably have, and a fair amount of download time), Shockwave (requires a plug-in installed in your Browser) or Java (requires Java, duh)

Fast Bob Regular Bob Slow Bob

Down on the surface of the water, what does it mean for the rings to be closer together? At a fixed point, what would someone floating there see and feel? Say, a duck, to continue our nature story. The duck would bob up and down as the waves passed under him. Since each ring is moving at the same, constant speed, if the rings are closer together, the duck will bob more frequently. If the rings are farther apart, the duck bobs less frequently. We can count the bobs, and thus define the frequency of the waves as the number of pulses per second passing a fixed point. High frequency in the direction of falcon source motion, low frequency behind the source motion.

Uh, you said something about stars.

I was getting to that. The broader relevance of these figures is that many things in nature turn out to be waves, if you look at them with enough technology and mathematics. In particular, sound and light are kinds of waves, as you've probably heard, but not thought much about. Mostly they are wave trains, rapid alternations following closely, not isolated pulses like a ring of water. Water waves can do this too, of course: we've mentioned only pulses so far to make things simpler. A nice point is that the same picture works for wave trains as for regular pulses, as shown above. You just have to imagine the circles as the successive peaks of the wave train.

Slow Bob Fast Bob

The physical wave nature of light and sound is important, because it's closely connected with how we see and hear them. Color and musical pitch (high and low notes) depend on how fast the the waves "wave". You may not see how color can be arranged from high to low like a musical keyboard, but you know that if you put white light, say sunlight, thru a prism, you get a rainbow of colors, a spectrum. This spectrum turns out to be just the arrangement from high to low frequency. Remember, this is how rapidly they "bob" or fluctuate at a fixed position, not how fast the waves spread from one place to another, which speed doesn't change for high and low frequencies. The low musical notes at the left of the keyboard, and the red end of the light spectrum, are the low frequency waves, and the high notes at the right end of the keyboard, and the violet end of the light spectrum, are the high frequency waves.

Catch the next wave!

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